From Eternity to Here

The Quest for the Ultimate Theory of Time

From Eternity to Here is a popular-level book on cosmology and the arrow of time, published by Dutton in January, 2010.

“For anyone who ever wondered about the nature of time and how it influences our universe, this book is a must read. It is beautifully written, lucid, and deep.”— Kip Thorne, Feynman Professor of Theoretical Physics at Caltech and author of Black Holes and Time Warps: Einstein’s Outrageous Legacy.

About the Author

Sean Carroll is a theoretical physicist at the California Institute of Technology. He received his Ph.D. from Harvard in 1993, and worked at MIT, the Institute for Theoretical Physics at UC Santa Barbara, and the University of Chicago before moving to Caltech. His research involves theoretical physics and astrophysics, focusing on issues in cosmology, field theory, and gravitation. He is the author of Spacetime and Geometry, a graduate-level textbook on general relativity; has produced a set of introductory lectures for The Teaching Company entitled Dark Matter and Dark Energy: The Dark Side of the Universe; and blogs regularly at Cosmic Variance. His lives in Los Angeles with his wife, writer Jennifer Ouellette.

The Book

Why do we remember the past, but not the future? Why don’t we meet people who grow younger as they age? Why do things, left by themselves, tend to become messier and more chaotic? What would Maxwell’s Demon say to a Boltzmann Brain?

The answers can be traced to the moment of the Big Bang — or possibly before.

Time pervades our lives — we keep track of it, lament its loss, put it to good use. The rhythms of our clocks and our bodies let us measure the passage of time, as a ruler lets us measure the distance between two objects. But unlike distances, time has a direction, pointing from past to future. From Eternity to Here examines this arrow of time, which is deeply ingrained in the universe around us. The early universe — the hot, dense, Big Bang — was very different from the late universe — cool, empty, expanding space — and that difference in felt in all the workings of Nature, from the melting of ice cubes to the evolution of species.

The arrow of time is easy to perceive, much harder to understand. Physicists appeal to the idea of entropy, the disorderliness of a system, which tends to increase according to the celebrated Second Law of Thermodynamics. But why was entropy ever small in the first place? That’s a question that has been tackled by thinkers such as Ludwig Boltzmann, Stephen Hawking, Richard Feynman, Roger Penrose, and Alan Guth, all the way back to Lucretius in ancient Rome. But the answer remains elusive.

The only way to understand the origin of entropy is to understand the origin of the universe — by asking what happened at the Big Bang, and even before. From Eternity to Here discusses how entropy relates to black holes, cosmology, information theory, and the existence of life. The book tells a story that starts in the kitchen, where we can turn eggs into omelets but never the other way around, and takes us to the edges of the universe. Modern discoveries in cosmology — dark energy and the accelerating universe — and quantum gravity — the possibility of time before the Big Bang — come together to suggest a picture of a multiverse in which the arrow of time emerges naturally from the laws of physics.

The book was published in hardcover on January 7, 2010. You can order from any major bookseller.

Contents

Prologue The nature of time, the importance of entropy, and the role of cosmology.

Part One: Time, Experience, and the Universe

The Past is Present MemoryTime has different meanings: a label on different moments, the duration between events, and a medium of change. We can think of the past, present, and future as equally real.

The Heavy Hand of EntropyThe direction of time is governed by the Second Law of Thermodynamics: in a closed system, entropy only increases or stays the same. Entropy measures the disorder of a system.

The Beginning and End of Time The evolution of the universe through time, beginning with a hot, dense Big Bang (which may not be the true beginning), expanding and forming stars and galaxies, eventually accelerating into emptiness.

Part Two: Time in Einstein’s Universe

Time is PersonalEinstein’s Special Theory of Relativity. You can’t go faster than the speed of light; you stay within a light cone in spacetime. Time measures the duration elapsed along different trajectories.

Time is FlexibleEinstein’s General Theory of Relativity. Spacetime is curved, which we experience as gravity. The curvature of spacetime underlies black holes and the expansion of the universe.

Looping Through TimeClosed timelike curves would allow you to visit the past without violating the rules of relativity. A time machine of this sort doesn’t necessarily lead to paradoxes, but might be impossible to create according to the laws of physics.

Part Three: Entropy and Time’s Arrow

Running Time BackwardsThe fundamental laws of physics, as we understand them, conserve information: the future and past can be predicted and retrodicted from perfect knowledge of the present state. Microscopic processes are reversible.

Entropy and DisorderLudwig Boltzmann discovered our modern understanding of entropy: the number of ways microscopic constituents can be arranged to form the same macroscopic system. It’s natural for entropy to increase, but only if we assume a “Past Hypothesis” that entropy started very low.

Information and LifeThe growth of entropy powers our experience of life: the ability to remember the past, to metabolize free energy, and to process information. Maxwell’s Demon illustrates the connection between entropy and information.

Recurrent NightmaresA finite system spends most of its time in high-entropy equilibrium, with occasional fluctuations to lower entropy. A finite universe that lasts for all time would behave just that way, and most observers would be disembodied “Boltzmann brains.”

Quantum TimeQuantum mechanics says that what we can observe is much less than what exists. The act of observation seems to be irreversible. One interpretation is that the irreversibility is only apparent, as we exist in “branches of the wave function” that lose touch with other branches.

Part Four: From the Kitchen to the Multiverse

Black Holes: The Ends of TimeStephen Hawking showed that black holes aren’t completely black: they emit radiation. That implies that they have entropy, and that they will eventually evaporate away. Black holes provide a crucial clue to the connection between entropy and gravity.

The Life of the UniverseNear the Big Bang, the entropy of the universe was extremely low. It grew as the universe expanded, as gravity pulled matter together to form stars, galaxies, and black holes. But it remains much smaller than it could be; a state of truly high entropy would look like empty space.

Inflation and the MultiverseThe smooth state of the early universe can be explained by inflation – a period of high-energy acceleration at very early times. But inflation itself requires that the universe began in a state of even lower entropy; by itself, it doesn’t answer our questions. It does open a new possibility in the form of eternal inflation and the multiverse.

The Past Through TomorrowThere are a number of possible explanations of our observed arrow of time, including fundamentally irreversible laws and a boundary condition outside the laws of physics. To explain the arrow using only reversible laws requires that we situate the universe we observe within a time-symmetric multiverse. This and other speculative scenarios are topics of ongoing research.

Epilogue
The origin of the universe and the arrow of time are major unsolved problems in our understanding of the natural world. But there is every reason to expect that they will someday be understood using the laws of physics. The quest to answer these questions helps make it all meaningful.

Appendix: Math

Commentary

Blurbs

“For anyone who ever wondered about the nature of time and how it influences our universe, this book is a must read. It is beautifully written, lucid, and deep.” –Kip Thorne

“Sean Carroll is a sure-footed guide through some of the most perplexing and fascinating insights of modern physics. His delightful From Eternity to Here is an accessible and engaging exploration of the mysteries of time, grappling with issues that will very likely play a critical role in the next major upheaval in our understanding of the cosmos.” –Brian Greene

“The meaning of time at a fundamental level remains one of the most elusive mysteries physicists encounter today. Sean Carroll presents our current understanding of time and the ways in which physical theories single out time, which continues to march forward. There isn’t a single agreed-upon answer to some of the more perplexing questions to which he exposes the reader, but there is an abundance of interesting excursions written in entertaining and engaging language that will keep fascinated those interested in profound questions in modern physics.” –Lisa Randall

“Sean Carroll’s From Eternity to Here provides a wonderfully accessible account of some of the most profound mysteries of modern physics. While you may not agree with all his conclusions, you will find the discussion fascinating, and taken to much deeper levels than is normal in a work of popular science.” –Sir Roger Penrose

Heather Demarest at The Philosopher’s Eye: “Carroll’s book is intended for a popular audience, and would be a worthwhile investment for any philosopher curious about physics-based approaches to the metaphysics of time.”

Alan Boyle at Cosmic Log, msnbc.com: “The last season of Lost might clear up some fictional time-travel mysteries, but the true mysteries of time can be found in a new book titled From Eternity to Here.”

The Geek Philosophers: “If you want a thoughtful, funny crash course on what time might be, how time travel might work, and what scientists currently think about the nature of spacetime and our specific relationship to it, read Sean Carroll’s From Eternity to Here.”

Review by John Walker at Fourmilab: “This book is a tour de force popular exposition of thermodynamics and statistical mechanics, which provides the best intuitive grasp of these concepts of any non-technical book I have yet encountered.”

Published Articles

Articles by other people, that is. For my own writings, see extra resources.

WIRED magazine, December 2009: “Armchair Einsteins will geek out at [Sean Carroll’s] audacious thesis… His writing is accessible and peppered with cultural references… But don’t be fooled by his mass-market approach: Carroll isn’t afraid to wade into topics that have befuddled even name-brand physicists.”

Reviews

Publisher’s Weekly (starred review): “No one is better equipped to take readers on a rollercoaster ride through time, space, and the origins of the universe than Caltech theoretical physicist Carroll… Carroll writes with verve and infectious enthusiasm, reminding readers that “science is a journey in which getting there is, without question, much of the fun.”

Kirkus Reviews: “A revealing look into the fourth and thorniest dimension… Carroll (Theoretical Physics/Caltech) has read all the literary and scientific writing on the subject but has plenty of his own opinions. In his debut, the author writes in accessible prose, so readers who make the effort will absorb an avalanche of information.”

Scientific American Book Club: “Sean Carroll is a scientist with a deep appreciation of the mystery of time: Why does it appear to “flow” from the past to the future and not vice versa? In From Eternity to Here, he offers an engaging tour of ideas from thermodynamics and cosmology, showing how they suggest a resolution.”

SEED: “In Carroll’s first book intended for popular audiences, the Caltech theoretical physicist delivers a masterful overview of what time is—and what its one-way passage implies about the nature of the universe. Unifying cosmology, thermodynamics, and information science into a refreshingly accessible whole, From Eternity to Here will make you wish time’s arrow could fly in reverse, if only so you could once again read the book for the first time.”

Associated Press: “This book should go down big with people who like discussing modern astronomy’s “black holes” that swallow everything nearby, and the Big Bang of more than 13 billion years ago that some experts believe created the universe.” (That’s about the highlight of the review, I’m afraid.)

Alexander Waugh, Wall Street Journal: “Outlines, in the simplest possible terms, all that is known about the arrow of time… The best way to grasp the rich mysteries of our universe is by constantly rereading the best and clearest explanations. Mr. Carroll’s From Eternity to Here is certainly one of them.”

Craig Callender, New Scientist: “Perhaps the best and most comprehensive discussion of time’s arrow that is widely accessible. Carroll explains time’s fascinating subtleties in a lucid and entertaining manner.”

Laurence A. Marschall, Natural History Magazine: “One of the most lucid popular overviews of modern theoretical cosmology that I have read in recent years.”

Justin Moyer, Washington Post: “Carroll keeps it real, getting at the complex guts of cutting-edge cosmology in discussions that will challenge fans of Hawking’s A Brief History of Time.”

Pedro Ferreira, Nature: “The book is a modern incarnation of the sort of works that twentieth-century physicists such as Arthur Eddington, Erwin Schrödinger and Werner Heisenberg wrote late in their lives — venerable, erudite accounts with a new, possibly esoteric idea to put across.”

Donna Bowman, The Onion‘s A.V. Club: “With equal parts patience, enthusiasm, and humor, Carroll presents a mini-course on the natural history of cosmology itself: what has been pieced together by evidence, then unraveled by new frames of reference, and the reasons we’re edging closer to answers even though scientific revolutions often seem to take us back to square one. Like all great teachers, he makes his subject irresistible, and makes his students feel smarter.”

D. Wayne Dworsky, San Francisco Book Review: “A world of stunning clarity; a quiescent moment in the universe to ponder our existence. His book invigorates the mind and leaves us in a state of awe. Don’t read another thing until you read this enduring testimony of reality.”

Excerpts

The prologue is reprinted here, to provide an overview of the themes of the book.

Errata

It happens to the best of us. Here are known mistakes in the hardcover edition of the book; hopefully they will be fixed in time for the paperback.

In Figure 3, on page 17, the label on the pendulum is wrong; it should read “86,400 oscillations”.

On page 39, the very first sentence, the Sun is half a degree across, not one degree across.

There is a big mistake in the last paragraph of page 85, continuing on to page 86. The orbiting clock in this example will actually experience less time, not more, even though it is freely-falling. The basic idea is that the longest-time path between two events is definitely a free-fall path, but the converse doesn’t hold; not every free-fall path experiences the longest time. In the updated version I’m using a different example, comparing a clock that stays stationary on Earth to one that is thrown directly upwards and comes back down; in that case the clock that is thrown really would experience more time.

On page 226, one third of the way down, “it’s still much more unlikely” should be the opposite — “it’s still much more likely”.

On page 338, first sentence of the last paragraph, the word “our” should be removed in “not what our the physical system”.

On page 389, there was an arithmetic mistake in the calculation of the dark energy in the volume of Lake Michigan. The correct answer is that there is about one food calorie’s worth of energy in the dark energy contained in that volume, not one calorie per cubic centimeter.

On page 391, in footnote 67, the last sentence, replace “we have make an arbitrary choice” with “we have made an arbitrary choice”.

On page 395, in footnote 110, von Neumann actually investigated cellular automata in the 1940’s, not the 1960’s. He died in 1957, but his major work in the field was published posthumously.